I had trouble getting edited and uploaded web pages to update. The reason was that my ISP caches web pages visited. So, regardless of whether the browser cache was empty or full, the 'Refresh page' would only query the ISP's cache. Usually, holding the Shift button down (CTRL for IE) will force the caching server to get the most current version of the page from the source server. It should override the browser cache too. Can't think why this wouldn't work but that was the basis for the previous suggestion made. Is there any other proxy involved between you and the Internet? Is the 'Direct connection to the Internet' option selected in 'Tools > Options > General > Connection Settings?
If there is a FF cache problem stopping this from working then there could be something wrong with the Profile (that's where the cache is located). The Profile can cause trouble for one reason or another and might need replacing. Perhaps create a new Profile to see if that clears the problem up. If it does, you could consider keeping it and building it up to requirements.
Just in case you have never created a new Profile before:
* It's always best to keep a copy of a healthy Profiles folder (empty the cache first). There are some useful files in it, especially Bookmarks.html.
* Here's the Mozilla page about Profiles.
* A good backup utility is MozBackup. It will extract some important file from the Profiles folder that can be later restored into a new Profile.